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Grade 9 Academic Math (MPM1D0) Summer Package
Pre-Requisite Algebra Skills
Content Page 1.1 Using variables 1
1.2 Exponents and Order of Operations 2
2.3 Multiplying and Dividing Rational Numbers 3
2.4 The Distributive Property 4
3.1 Solving Two-Step Equations 5
3.2 Solving Multi-Step Equations 6
3.3 Equations with variables on both sides 7
3.4 Ratio and Proportion 8
3.6 Equations and Problem Solving 9
3.7 Percent of Change 10
3.9 Pythagorean Theorem 11
Fraction Addition and Subtraction 12
Fraction Addition and Subtraction (Mixed Numbers) 13
Fraction Multiplication 14
Fraction Division 15
Answers 16 - 17
Practice 1-1 Using Variables
Write an algebraic expression for each phrase.
1. 7 increased by x 2. p multiplied by 3
3. 10 decreased by m 4. n less than 7
5. the product of 2 and q 6. 3 more than m
Write a phrase for each algebraic expression.
7. 8. s – 10 9. x + 13 10. ab + 2
Define a variable and write an algebraic expression for each phrase.
11. the difference of 8 and a number 12. the sum of 4 and a number
13. the product of 2 and a number 14. 3 increased by a number
15. 10 plus the quotient of a number and 15 16. 12 less than a number
Define a variable and write an algebraic equation to model each situation.
17. What is the total cost of buying several shirts at $24.95 each?
18. The number of gal of water used to water trees is 30 times the numberof trees.
19. What is the amount of money in a bank containing only dimes?
20. What is the number of marbles left in a 48-marble bag after somemarbles have been given away?
21. The total cost equals the price of the tickets multiplied by eight people.
22. What is the cost of buying several pairs of pants at $32.95 per pair?
Define variables and write an equation to model the relationship in each table.
Write an equation to model each situation. Then solve.
7. You want to buy a bouquet of yellow roses and baby’s breath for $16.The baby’s breath costs $3.50 per bunch, and the roses cost $2.50 each.You want one bunch of baby’s breath and some roses for your bouquet.How many roses can you buy?
8. Suppose you walk at the rate of 210 ft/min. You need to walk 10,000 ft.How many more minutes will it take you to finish if you have alreadywalked 550 ft?
9. Suppose you have shelled 6.5 lb of pecans, and you can shell pecans at arate of 1.5 lb per hour. How many more hours will it take you to shell atotal of 11 lb of pecans?
10. To mail a first class letter, the U.S. Postal Service charges $.34 for thefirst ounce and $.21 for each additional ounce. It costs $1.18 to mailyour letter. How many ounces does your letter weigh?
11. Suppose you want to buy one pair of pants and several pairs of socks.The pants cost $24.95, and the socks are $5.95 per pair. How many pairs of socks can you buy if you have $50.00 to spend?
Write an equation to model each situation. Then solve.
46. The attendance at a baseball game was 400 people. Student tickets cost$2 and adult tickets cost $3. Total ticket sales were $1050. How manytickets of each type were sold?
47. The perimeter of a pool table is 30 ft. The table is twice as long as it iswide. What is the length of the pool table?
48. Lopez spent of his vacation money for travel and of his vacationmoney for lodging. He spent $1100 for travel and lodging. What is thetotal amount of money he spent on his vacation?
49. Victoria weighs as much as Mario. Victoria weighs 125 lb. How muchdoes Mario weigh?
50. Denise’s cell phone plan is $29.95 per month plus $.10 per minute foreach minute over 300 minutes of call time. Denise’s cell phone bill is$99.95. For how many minutes was she billed?
Write an equation to model each situation. Then solve. Check your answer.
34. Hans needs to rent a moving truck. Suppose Company A charges a rateof $40 per day and Company B charges a $60 fee plus $20 per day. Forwhat number of days is the cost the same?
35. Suppose a video store charges nonmembers $4 to rent each video. Astore membership costs $21 and members pay only $2.50 to rent eachvideo. For what number of videos is the cost the same?
36. Suppose your club is selling candles to raise money. It costs $100 to rent a booth from which to sell the candles. If the candles cost your club $1 each and are sold for $5 each, how many candles must be sold to equal your expenses?
Find the value of x.
37. 38. 39.
(1.15 � 0.8x)° (2.3 � 1.5x)°( x � 3)°14 ( x � 7)°3
4(4x � 2)° (5x � 3)°
35
34
12
23
56
34
23
34
34
23
12
14
12
14
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(Answers on page 16-17)
Practice 3-4 Ratio and Proportion
Find each unit rate.
1. $60 for 8 h 2. 3. 4.
5. An 8-ounce bottle of lotion costs $4.50. What is the cost per ounce?
6. A pound of coffee costs $14.99. What is the cost per ounce?
Which pairs of ratios could form a proportion? Justify your answer.
7. 8. 9. 10. 11.
Solve each proportion.
12. 13. 14. 15.
16. 17. 18. 19.
20. 21. 22. 23.
24. 25. 26. 27.
28. 29. 30. 31.
32. 33. 34. 35.
36. 37.
38. 39.
40. 41.
42. You are riding your bicycle. It takes you 28 min to go 8 mi. If youcontinue traveling at the same rate, how long will it take you to go 15 mi?
43. Suppose you traveled 84 mi in 1.5 h. Moving at the same speed, howmany mi would you cover in 3 h?
44. A canary’s heart beats 130 times in 12 s. Use a proportion to find howmany times its heart beats in 50 s.
45. Your car averages 18 mi per gal on the highway. If gas costs $1.85 per gal, how much does it cost in dollars per mi to drive your car on the highway?
1. A passenger train’s speed is 60 mi/h, and a freight train’s speed is 40 mi/h. The passenger train travels the same distance in 1.5 h less timethan the freight train. How long does each train take to make the trip?
2. Lois rode her bike to visit a friend. She traveled at 10 mi/h. While shewas there, it began to rain. Her friend drove her home in a car travelingat 25 mi/h. Lois took 1.5 h longer to go to her friend’s than to returnhome. How many hours did it take Lois to ride to her friend’s house?
3. May rides her bike the same distance that Leah walks. May rides herbike 10 km/h faster than Leah walks. If it takes May 1 h and Leah 3 h totravel that distance, how fast does each travel?
4. The length of a rectangle is 4 in. greater than the width. The perimeterof the rectangle is 24 in. Find the dimensions of the rectangle.
5. The length of a rectangle is twice the width. The perimeter is 48 in. Findthe dimensions of the rectangle.
6. At 10:00 A.M., a car leaves a house at a rate of 60 mi/h. At the sametime, another car leaves the same house at a rate of 50 mi/h in theopposite direction. At what time will the cars be 330 miles apart?
7. Marla begins walking at 3 mi/h toward the library. Her friend meets her at the halfway point and drives her the rest of the way to the library. The distance to the library is 4 miles. How many hours did Marla walk?
8. Fred begins walking toward John’s house at 3 mi/h. John leaves hishouse at the same time and walks toward Fred’s house on the samepath at a rate of 2 mi/h. How long will it be before they meet if thedistance between the houses is 4 miles?
9. A train leaves the station at 6:00 P.M. traveling west at 80 mi/h. On aparallel track, a second train leaves the station 3 hours later travelingwest at 100 mi/h. At what time will the second train catch up with the first?
10. It takes 1 hour longer to fly to St. Paul at 200 mi/h than it does to returnat 250 mi/h. How far away is St. Paul?
11. Find three consecutive integers whose sum is 126.
12. The sum of four consecutive odd integers is 216. Find the four integers.
13. A rectangular picture frame is to be 8 in. longer than it is wide. Dennisuses 84 in. of oak to frame the picture. What is the width of the frame?
14. Each of two congruent sides of an isosceles triangle is 8 in. less thantwice the base. The perimeter of the triangle is 74 in. What is the lengthof the base?
Find each percent of change. Describe the percent of change as an increaseor decrease. Round to the nearest whole number.
1. 36 g to 27 g 2. 40 cm to 100 cm 3. 90 in. to 45 in. 4. 500 lb to 1500 lb
5. $90 to $84.50 6. $100 to $140 7. $15 to $5.50 8. 100 mi to 175 mi
9. 280 m to 320 m 10. 58 to 76 11. 60 to 150 12. 600 mi to 480 mi
13. 18 to 27 14. 290 yd to 261 yd 15. 26.2 to 22.8 16. $8.50 to $12.75
17. to 18. to 19. to 20. to
Find each percent of change. Describe the percent of change as an increaseor decrease. Round to the nearest whole number.
21. In 1985, the average price for gasoline was $1.20/gal. In 2000, theaverage price for gasoline was $1.56. Find the percent of change.
22. In 1980, Texas had 27 U.S. Representatives. That number increased to 30 in 2000. Find the percent of change.
23. In 1980, the average annual tuition charge for a four-year publicuniversity was $840. The average annual tuition charge in 2000 was$3356. What is the percent of change?
24. The United States imported 6,909,000 barrels of oil per day in 1980. In2000, the United States imported 11,459,000 barrels of oil per day. Whatis the percent of change?
25. In 1977, the average number of households with cable television was16.6%. In 2000, the average number of households with cable televisionwas 68%. What is the percent of change?
26. In 1989, there were 38,000 licensed drivers under the age of 16. In 1999,the total number of licensed drivers under 16 was 33,248. Find thepercent of change.
27. In 1990, Atlanta, GA, failed to meet air quality standards on 42 days.In 1999, Atlanta failed to meet air quality standards on 61 days. What isthe percent of change?
Find the greatest possible error and the percent error for each measurement.
28. 3 cm 29. 0.5 cm 30. 6 cm
31. 16 in. 32. 36.85 g 33. 0.9 cm
Find the minimum and maximum possible areas for rectangles with thefollowing measurements.
34. 8 cm 3 10 cm 35. 3 in. 3 5 in. 36. 8 m 3 12 m
Find the minimum and maximum possible volume for a rectangular solidwith the following measurements.
37. 16 in. 3 22 in. 3 18 in. 38. 13 cm 3 15 cm 3 18 cm 39. 3 m 3 4 m 3 5 m
39. A ladder is 25 ft long. The ladder needs to reach to a window that is24 ft above the ground. How far away from the building should thebottom of the ladder be placed?
40. Suppose you are making a sail in the shape of a right triangle for asailboat. The length of the longest side of the sail is 65 ft. The sail is tobe 63 ft high. What is the length of the third side of the sail?
41. Suppose you leave your house and travel 13 mi due west. Then youtravel 3 mi due south. How far are you from your house?
42. A wire is run between the tips of two poles. One pole is 23 ft taller thanthe other pole. The poles are 37 ft apart. How long does the wire needto be to reach between the two poles?
43. A 20-ft-long wire is used to support a television antenna. The wire isconnected to the antenna 15 ft above the ground. How far away fromthe base of the tower will the other end of the wire be located?
Fractions: Addition and Subtraction (Mixed Numbers)
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Fractions: Multiplication
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Fractions: Division
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Practice 1-11.7±x 2.3p 3.10—rn 4.7—n5. 2q 6. m + 3 7. 8 divided by a 8. 10 less than s9. 13 more than x 10. 2 more than the product of a and b11.8—n 12.4±n 13.2n 14.3±n 15.1O+f16. n — 12 17. c = 24.95s 18. g = 30t 19. m = O.lOd20. n = 48 — g 21. c 8p 22. c = 32.95p23—28. Choice of variables may vary.
t — number of tickets, c = total cost;h = number of hours, d = distance:h = number of hours,p — total pay:C = change, a = total cost;d = number of days, I = length;r = miles traveled, t = miles remaining
23. c = 3.50t 24. d = 55h 25. p = 5h 26. a = 10 — c27. 1 = O.45d 28. r = 500 — t